9,979 research outputs found
Boundary value problems for noncompact boundaries of Spinᶜ manifolds and spectral estimates
We study boundary value problems for the Dirac operator on Riemannian
Spin manifolds of bounded geometry and with noncompact boundary. This
generalizes a part of the theory of boundary value problems by C. B\"ar and W.
Ballmann for complete manifolds with closed boundary. As an application, we
derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of
the boundary, for the spectrum of the Dirac operator on the noncompact boundary
of a Spin manifold. The limiting case is then studied and examples are then
given.Comment: Accepted in Proceedings of the London Mathematical Societ
The \beta-function in duality-covariant noncommutative \phi^4-theory
We compute the one-loop \beta-functions describing the renormalisation of the
coupling constant \lambda and the frequency parameter \Omega for the real
four-dimensional duality-covariant noncommutative \phi^4-model, which is
renormalisable to all orders. The contribution from the one-loop four-point
function is reduced by the one-loop wavefunction renormalisation, but the
\beta_\lambda-function remains non-negative. Both \beta_\lambda and
\beta_\Omega vanish at the one-loop level for the duality-invariant model
characterised by \Omega=1. Moreover, \beta_\Omega also vanishes in the limit
\Omega \to 0, which defines the standard noncommutative \phi^4-quantum field
theory. Thus, the limit \Omega \to 0 exists at least at the one-loop level.Comment: 11 pages, LaTe
Breaking of axial symmetry in excited heavy nuclei as identified in Giant Dipole Resonance data
A recent theoretical prediction of a breaking of axial symmetry in quasi all
heavy nuclei is confronted to a new critical analysis of photon strength
functions of nuclei in the valley of stability. For the photon strength in the
isovector giant dipole resonance (IVGDR) regime a parameterization of GDR
shapes by the sum of three Lorentzians (TLO) is extrapolated to energies below
and above the IVGDR. The impact of non-GDR modes adding to the low energy slope
of photon strength is discussed including recent data on photon scattering and
other radiative processes. These are shown to be concentrated in energy regions
where various model calculations predict intermediate collective strength; thus
they are obviously separate from the IVGDR tail. The triple Lorentzian (TLO)
ansatz for giant dipole resonances is normalized in accordance to the dipole
sum rule. The nuclear droplet model with surface dissipation accounts well for
positions and widths without local, nuclide specific, parameters. Very few and
only global parameters are needed when a breaking of axial symmetry already in
the valley of stability is admitted and hence a reliable prediction for
electric dipole strength functions also outside of it is expected.Comment: 21 pages, 21 figures, PACS: 26.50.+x, 25.20.Dc,27.60.+j Accepted by
Europ. Phys. Journal
Impact of Triaxiality on the Emission and Absorption of Neutrons and Gamma Rays in Heavy Nuclei
For many spin-0 target nuclei neutron capture measurements yield information
on level densities at the neutron separation energy. Also the average photon
width has been determined from capture data as well as Maxwellian average cross
sections for the energy range of unresolved resonances. Thus it is challenging
to use this data set for a test of phenomenological prescriptions for the
prediction of radiative processes. An important ingredient for respective
calculations is the photon strength function for which a parameterization was
proposed using a fit to giant dipole resonance shapes on the basis of
theoretically determined ground state deformations including triaxiality.
Deviations from spherical and axial symmetry also influence level densities and
it is suggested to use a combined parameterization for both, level density and
photon strength. The formulae presented give a good description of the data for
low spin capture into 124 nuclei with 72<A<244 and only very few global
parameters have to be adjusted when the predetermined information on ground
state shapes of the nuclei involved is accounted for.Comment: Contribution to the Proceedings of Scientific Workshop on Nuclear
Fission Theory-2, November 2012 at Biarritz, Franc
Importance of nuclear triaxiality for electromagnetic strength, level density and neutron capture cross sections in heavy nuclei
Cross sections for neutron capture in the range of unresolved resonances are
predicted simultaneously to level distances at the neutron threshold for more
than 100 spin-0 target nuclei with A >70. Assuming triaxiality in nearly all
these nuclei a combined parameterization for both, level density and photon
strength is presented. The strength functions used are based on a global fit to
IVGDR shapes by the sum of three Lorentzians adding up to the TRK sum rule and
theory-based predictions for the A-dependence of pole energies and spreading
widths. For the small spins reached by capture level densities are well
described by only one free global parameter; a significant collective
enhancement due to the deviation from axial symmetry is observed. Reliable
predictions for compound nuclear reactions also outside the valley of stability
as expected from the derived global parameterization are important for nuclear
astrophysics and for the transmutation of nuclear waste.Comment: Contribution to the proceedings of the ERINDA workshop held at CERN
in October 2013 with modification
Functional Renormalization of Noncommutative Scalar Field Theory
In this paper we apply the Functional Renormalization Group Equation (FRGE)
to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar.
We derive the flow equation in the matrix representation and discuss the theory
space for the self-dual model. The features introduced by the external
dimensionful scale provided by the non-commutativity parameter, originally
pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a
technical assumption, but without resorting to any truncation, it is then shown
that the theory is asymptotically safe for suitably small values of the
coupling, recovering the result of \cite{disertori:2007}. Finally, we
show how the FRGE can be easily used to compute the one loop beta-functions of
the duality covariant model.Comment: 38 pages, no figures, LaTe
On Finite 4D Quantum Field Theory in Non-Commutative Geometry
The truncated 4-dimensional sphere and the action of the
self-interacting scalar field on it are constructed. The path integral
quantization is performed while simultaneously keeping the SO(5) symmetry and
the finite number of degrees of freedom. The usual field theory UV-divergences
are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove
Spin dependent fragmentation function at Belle
The measurement of the so far unknown chiral-odd quark transverse spin
distribution in either semi-inclusive DIS (SIDIS) or inclusive measurements in
pp collisions at RHIC has an additional chiral-odd fragmentation function
appearing in the cross section. These chiral-odd fragmentation functions (FF)
can for example be the so-called Collins FF or the Interference FF. HERMES has
given a first hint that these FFs are nonzero, however in order to measure the
transversity one needs these FFs to be precisely known. We have used 29.0
fb of data collected by the Belle experiment at the KEKB
collider to measure azimuthal asymmetries for different charge combinations of
pion pairs and thus access the Collins FF.Comment: Results presented at the DIS 2006 conference in Tsukuba, Japa
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